document.write( "Question 1013511: Hello!
\n" ); document.write( "How do I solve this polynomial with the real number system?
\n" ); document.write( "2x^3+3x^2 +2x +3=0\r
\n" ); document.write( "\n" ); document.write( "Please help me as soon as you can!
\n" ); document.write( "Thank you very much! \n" ); document.write( "
Algebra.Com's Answer #629813 by rothauserc(4718)\"\" \"About 
You can put this solution on YOUR website!
Using the rational zeros test on
\n" ); document.write( "2x^3 +3x^2 +2x +3 = 0
\n" ); document.write( "the constant is 3 with 1, 3 as factors
\n" ); document.write( "the constant of the x^3 term is 2 so we have
\n" ); document.write( "possible zeros are + or - 1/2 and 3/2 = -1/2, -3/2, 1/2, 3/2
\n" ); document.write( "let's try -3/2
\n" ); document.write( "2*(-3/2)^3 +3*(-3/2)^2 +2(-3/2) + 3 = 0
\n" ); document.write( "-27/4 +27/4 -3 +3 = 0
\n" ); document.write( "0 = 0
\n" ); document.write( "we now know that -1.5 is one of our roots
\n" ); document.write( "next is to do synthetic division
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\n" ); document.write( "1.5 | 2 3 2 3 |
\n" ); document.write( ": 3 9 16.5
\n" ); document.write( ":::: 2 6 11 19.5
\n" ); document.write( "therefore the 2nd degree polynomial is
\n" ); document.write( "2x^2 + 6x + 11 + (19.5 / (x - 1.5))
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\n" ); document.write( "the rational root is x = -1.5
\n" ); document.write( "also there are two imagery roots i and -i
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\n" ); document.write( "Solve for x
\n" ); document.write( "2x^3 +3x^2 +2x +3 = 0
\n" ); document.write( ":
\n" ); document.write( "The left hand side factors into a product with two terms:
\n" ); document.write( "(2x+3) (x^2+1) = 0
\n" ); document.write( ":
\n" ); document.write( "Split into two equations:
\n" ); document.write( "2x+3 = 0 or x^2+1 = 0
\n" ); document.write( ":
\n" ); document.write( "Subtract 3 from both sides:
\n" ); document.write( "2x = -3 or x^2+1 = 0
\n" ); document.write( ":
\n" ); document.write( "Divide both sides by 2:
\n" ); document.write( "x = -3/2 or x^2+1 = 0
\n" ); document.write( ":
\n" ); document.write( "Subtract 1 from both sides:
\n" ); document.write( "x = -3/2 or x^2 = -1
\n" ); document.write( ":
\n" ); document.write( "Take the square root of both sides:
\n" ); document.write( "*****************************************
\n" ); document.write( "x = -3/2 or x = i or x = -i
\n" ); document.write( " \n" ); document.write( "
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